<span>use De Moivre's Theorem:
⁵√[243(cos 260° + i sin 260°)] = [243(cos 260° + i sin 260°)]^(1/5)
= 243^(1/5) (cos (260 / 5)° + i sin (260 / 5)°)
= 3 (cos 52° + i sin 52°)
z1 = 3 (cos 52° + i sin 52°) ←← so that's the first root
there are 5 roots so the angle between each root is 360/5 = 72°
then the other four roots are:
z2 = 3 (cos (52 + 72)° + i sin (52+ 72)°) = 3 (cos 124° + i sin 124°)
z3 = 3 (cos (124 + 72)° + i sin (124 + 72)°) = 3 (cos 196° + i sin 196°)
z4 = 3 (cos (196 + 72)² + i sin (196 + 72)°) = 3 (cos 268° + i sin 268°)
z5 = 3 (cos (268 + 72)° + i sin (268 + 72)°) = 3 (cos 340° + i sin 340°) </span>
Answer: After 1 year: $5,610
After 2 years: $5,722.20
Step-by-step explanation: Use the formula for periodic compounding interest, which is
A = P(1 + r/n)^(nt), where A is the final amount, P is the initial deposit, r is the interest rate as a decimal, n is the number of times the interest is compounded per year, and t is how many years.
Here, P = 5,500, r = 0.02 (that's 2% as a decimal), n = 1,
t = 1 for the first answer, t = 2 for the second answer (1 year, then for 2 years)
Plug the known values in to solve...
For 1 year...
A = 5,500(1 + 0.02/1)^(1*1)
A = 5,500(1.02)^1
A = 5,610
For 2 years...
A = 5,500(1 + 0.02/1)^(1*2)
A = 5,500(1.02)²
A = 5,722.20
Step-by-step explanation:
x + 8a = 25 + ax - 7a
x = 5
5 + 8a = 25 + 5a - 7a
5 + 8a = 25 - 2a
5 + 10a = 25
10a = 20
a = 2
Answer:
2(2-10)/3=x
Step-by-step explanation:
2(2-10)=3x
2(2-10)/3=x
Answer:
4/6 of the cake is left
Steps down below
Step-by-step explanation:
How i got the answer:
As we know that the question is asking how much, so and we also know that Susan ate 1/5 of 5/6 so the and for the equation will be 1/6. So 5/6 - 1/6 will give you the correct answer for this question.
Steps:
1: Subtract the numbers so 5/6 subtract 1/6 =4/6
Answer: 4/6
<em><u>Hope this helps.</u></em>
